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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationMon, 01 Dec 2008 11:27:29 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/01/t1228156086ebxhxovrg6ud0xc.htm/, Retrieved Sun, 05 May 2024 13:06:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27100, Retrieved Sun, 05 May 2024 13:06:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F       [Law of Averages] [q3 / 7] [2008-11-30 17:25:28] [4300be8b33fd3dcdacd2aa9800ceba23]
F           [Law of Averages] [Non Stationary Ti...] [2008-12-01 18:27:29] [3bb0537fcae9c337e49b9ce75ff3d4da] [Current]
Feedback Forum
2008-12-08 11:51:21 [Ellen Smolders] [reply] 
De student heeft deze vraag correct beantwoord. Iets meer uitleg over de matric:
De VRM gaat trachten om de spreading van de tijdreeks te verkleinen door te differentiëren, d staat voor een gewone differentiatie terwijl D staat voor een seizoenale differentiatie. De eerste kolom in de matric geeft aan hoe vaak er gewoon gedifferentieerd is en hoe vaak seizonaal gedifferentieerd. De 2e kolom geeft de variantie van onze tijdreeks weer, we moeten zoals eerder vermeld kijken naar de kleinste spreiding om een zo stationair mogelijke tijdreeks te bekomen, de optimale spreiding bekomen we bij 1.00197181511618, dus na 1 keer gewoon te differentiëren en geen enkele keer seizonaal.

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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27100&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27100&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27100&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)245.789579158317Range53Trim Var.208.320981148584
V(Y[t],d=1,D=0)0.995243499046285Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.7741935483871Range8Trim Var.2.64158032877469
V(Y[t],d=0,D=1)14.9318174167705Range18Trim Var.7.32641134751773
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.03297272071613Range8Trim Var.2.31112097669256
V(Y[t],d=3,D=1)11.9668739882423Range16Trim Var.6.8665239615866
V(Y[t],d=0,D=2)27.4132153914197Range28Trim Var.12.8127953471465
V(Y[t],d=1,D=2)6.30335332000888Range8Trim Var.2.74308522971943
V(Y[t],d=2,D=2)12.1352887128572Range16Trim Var.6.40267558528428
V(Y[t],d=3,D=2)36.1016949152542Range28Trim Var.22.8327340716238

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 245.789579158317 & Range & 53 & Trim Var. & 208.320981148584 \tabularnewline
V(Y[t],d=1,D=0) & 0.995243499046285 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.95571824521426 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.7741935483871 & Range & 8 & Trim Var. & 2.64158032877469 \tabularnewline
V(Y[t],d=0,D=1) & 14.9318174167705 & Range & 18 & Trim Var. & 7.32641134751773 \tabularnewline
V(Y[t],d=1,D=1) & 2.09046737816987 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 4.03297272071613 & Range & 8 & Trim Var. & 2.31112097669256 \tabularnewline
V(Y[t],d=3,D=1) & 11.9668739882423 & Range & 16 & Trim Var. & 6.8665239615866 \tabularnewline
V(Y[t],d=0,D=2) & 27.4132153914197 & Range & 28 & Trim Var. & 12.8127953471465 \tabularnewline
V(Y[t],d=1,D=2) & 6.30335332000888 & Range & 8 & Trim Var. & 2.74308522971943 \tabularnewline
V(Y[t],d=2,D=2) & 12.1352887128572 & Range & 16 & Trim Var. & 6.40267558528428 \tabularnewline
V(Y[t],d=3,D=2) & 36.1016949152542 & Range & 28 & Trim Var. & 22.8327340716238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27100&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]245.789579158317[/C][C]Range[/C][C]53[/C][C]Trim Var.[/C][C]208.320981148584[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.995243499046285[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.95571824521426[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5.7741935483871[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.64158032877469[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]14.9318174167705[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]7.32641134751773[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.09046737816987[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4.03297272071613[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.31112097669256[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.9668739882423[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.8665239615866[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.4132153914197[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.8127953471465[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.30335332000888[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.74308522971943[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]12.1352887128572[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.40267558528428[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]36.1016949152542[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]22.8327340716238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27100&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27100&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Variance Reduction Matrix
V(Y[t],d=0,D=0)245.789579158317Range53Trim Var.208.320981148584
V(Y[t],d=1,D=0)0.995243499046285Range2Trim Var.NA
V(Y[t],d=2,D=0)1.95571824521426Range4Trim Var.0
V(Y[t],d=3,D=0)5.7741935483871Range8Trim Var.2.64158032877469
V(Y[t],d=0,D=1)14.9318174167705Range18Trim Var.7.32641134751773
V(Y[t],d=1,D=1)2.09046737816987Range4Trim Var.0
V(Y[t],d=2,D=1)4.03297272071613Range8Trim Var.2.31112097669256
V(Y[t],d=3,D=1)11.9668739882423Range16Trim Var.6.8665239615866
V(Y[t],d=0,D=2)27.4132153914197Range28Trim Var.12.8127953471465
V(Y[t],d=1,D=2)6.30335332000888Range8Trim Var.2.74308522971943
V(Y[t],d=2,D=2)12.1352887128572Range16Trim Var.6.40267558528428
V(Y[t],d=3,D=2)36.1016949152542Range28Trim Var.22.8327340716238


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(x,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')